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Tuesday, March 4, 2014

Independent Samples t Tests with SPSS

In this paper, I will discuss the statistical assumptions of the independent samples t test as well as present a brief summation of results based on the SPSS analysis of the given data set.

Statistical Assumptions

The three assumptions underlying the independent-samples t test are that the test variable has a normal distribution in both populations of study; both populations have approximately equal variances; and both samples are randomly selected from the population and the observations in each sample are independent of the other (each has no influence on the other) (Green & Salkind, 2014).

Dependent and Independent Variables and Null and Alternative Hypothesis

I have used race of the respondents as the independent variable and how often respondent attends religious services as the dependent variable.

The null hypothesis is: Race (Black or White) does not influence frequency of attendance at religious services.

The confidence level is .95. In this example, the variances are similar and consequently, the standard t test, t(1390) = -7.0, p = .00, and the t test for unequal variances, t(325.5) = -7.64, p = .00 yield similar results. I reject the null hypothesis: Race has an effect on how often respondents attend religious services, and in this case, Blacks attend religious services more frequently than Whites.

An independent-samples t test was conducted to evaluate whether race (Black or White) influences attendance at religious services. The test was significant, and the results were in agreement with the alternative hypothesis. The 95% confidence interval for the difference in means was quite narrow, ranging from -1.78 to -1.0. This means there is a 95% chance that the confidence interval range contains the true population mean. The eta square index indicated that 3% (η2 =.03) of the variance of the attendance variable was accounted for by whether the respondent was White or Black. The effect was small to medium.

Syntax and Output Files

T-TEST
GROUPS=RACE(1 2)

/MISSING=ANALYSIS

/VARIABLES=ATTEND

/CRITERIA=CI(.95).

T-Test

Notes

Output Created

25-JAN-2014
09:31:44

Comments

Input

Data

C:\Users\Deborah\Desktop\Stats\gss04student_corrrected.sav

Active Dataset

DataSet1

Filter

<none>

Weight

<none>

Split File

<none>

N of Rows in Working Data File

1500

Missing Value Handling

Definition of Missing

User defined missing values are treated as missing.

Cases Used

Statistics for each analysis are based on the cases with no
missing or out-of-range data for any variable in the analysis.